A GARCH Model of the Implied Volatility of the Swiss Market Index From Option Pricesdffrom Options Prices

This paper estimates the implied stochastic process of the volatility of the Swiss market index (SMI) from the prices of options written on it. A GARCH(1,1) model is shown to be a good parameterization of the process. Then, using the GARCH option pricing model of Duan (1991), the implied volatility process is estimated by a simulation minimization method from option price data. We find the persistence of volatility shocks implied by options on the SMI to be very close to that estimated from historical data on the index itself. Comparing the performances of the implied GARCH option pricing model to that of the Black and Scholes model it appears that the overall pricing performance of the former is superior. However the large sample standard deviations of the out-of-sample pricing errors suggest that this result should be taken with caution.

[1]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[2]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[3]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[4]  Thomas H. McCurdy,et al.  Testing the Martingale Hypothesis in Deutsche Mark Futures with Models Specifying the Form of Heteroskedasticity , 1988 .

[5]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[6]  Richard T. Baillie,et al.  Stock Returns and Volatility , 1990, Journal of Financial and Quantitative Analysis.

[7]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[8]  Adrian Pagan,et al.  The econometrics of financial markets , 1996 .

[9]  M. Rubinstein..  Displaced Diffusion Option Pricing , 1983 .

[10]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[11]  Guy Laroque,et al.  Estimation of multi-market fix-price models: an application of pseudo maximum likelihood methods , 1989 .

[12]  Daniel B. Nelson,et al.  Inequality Constraints in the Univariate GARCH Model , 1992 .

[13]  J. Laffont,et al.  ECONOMETRICS OF FIRST-PRICE AUCTIONS , 1995 .

[14]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[15]  R. Engle,et al.  Implied ARCH models from options prices , 1992 .

[16]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[17]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[18]  R. Engle,et al.  Semiparametric ARCH Models , 1991 .

[19]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[20]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[21]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[22]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[23]  Michael J. Brennan,et al.  The Pricing of Contingent Claims in Discrete Time Models , 1979 .

[24]  B. Mandelbrot.  The Variation of Some Other Speculative Prices , 1967 .

[25]  J. Duan.  THE GARCH OPTION PRICING MODEL , 1995 .

[26]  Mark Rubinstein,et al.  The Valuation of Uncertain Income Streams and the Pricing of Options , 1976 .

[27]  Richard J. Rendleman,et al.  STANDARD DEVIATIONS OF STOCK PRICE RATIOS IMPLIED IN OPTION PRICES , 1976 .

[28]  Alain Monfort,et al.  Simulation-based inference: A survey with special reference to panel data models , 1993 .

[29]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .